CozumelMyCozumel has a whole forum dedicated to things to do on the island. Things like:
Take the tours of San Gervasio, the Mayan Ruins, and the Tequila tour.
Spend a day at Chankanaab, walk through the Archeological exhibit, the Botanical Gardens, snorkle, see the Dolphin show, or just veg on the beach.
Go to Punta Sur Park, take the boat tour of the Mangrove Swamp to see the crocodiles, snorkel at the park (some of the very best snorkeling you can do on Cozumel without a boat).
Take the tour of Kaokao, the Chocolate Factory, learn how chocolate is made, buy some Mexican chocolate at the gift store.
Have breakfast at the Museum restaurant, then tour the Museum.
Go up to the Mercado on 25, wander through the stalls of the vendors, buy a Molcajete with the tejolote, for making your own guacamole or salsa (or grinding peppers and seeds for your own mole, if you are ambitious), some local artwork, or a hammock to take home. And have lunch at one of the little stalls -- delicious home made pozole, or, if you are really lucky, cochinita pibil or pava en relleno negro (a traditional Yucatan Turkey Stew, with a sauce made with black achiote paste - I adore that sauce).
Take a day trip to the mainland - Ferry to Playa Del Carmen, rent a car and drive down to Tulum to see the Mayan ruins right on the ocean, to Akumal to snorkel with sea turtles, or to Xel Ha.
Rent a car, or hire a taxi for the day, and drive around the Island, visit the wild East Side, with stop offs at the Rasta Bar, Coconuts, Chen Rio, and any of the blow holes that dot the East side, spouting up water when the surf rolls in. You can also take a detour off the main road on the West side on your way South to visit Cedral, a small local village a few kilometers in from the coast. And stop at Mezcalitos at the East end of the Transversal for a Margarita and some delicious barbecued shrimp.